According to the theory of algebra, this paper confirms that the Mejia and Rousselle model employing the conventional parameter estimation procedure fails to preserve the historical moments as anticipated. The cause of the failure is identified. For each stage of disaggregation, two corrected moment estimates for use in parameter estimation are proposed. The first estimate is derived based on making the parameter estimation equations mathematically consistent; the second estimate, on maintaining the linear relationship between the disaggregated flows and the flows being disaggregated. Using the proposed, corrected parameter estimation procedure, the moments of interest and additivity are preserved exactly in an expected value sense. Applications given also show that the proposed procedure has advantages over the conventional procedure.